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Scientific Reports volume 14, Article number: 3644 (2024 ) Cite this article

We propose detecting the moment an atom emits a photon by means of a nearly classical macroscopic clock and discuss its viability. It is shown that what happens in such a measurement depends on the relation between the clock’s accuracy and the width of the energy range available to the photon. Implications of the analysis for the long standing Schrödinger’s cat problem are reported.

In non-relativistic quantum mechanics, time is a mere parameter, quite distinct from the dynamical variables such as positions and momenta, conveniently represented by Hermitian operators. This often complicates the queries, easily answered in the classical context (a good overview has been given in Refs.1 and2). When does a quantum particle arrive at a given location (see Egusquiza, Muga and Baute in1 and Galapon in2)? How much time does a tunnelling particle spend in the barrier (see, e.g.,3,4)? How long does a quantum jump take (see Schulman, in5 and Refs. therein)? These questions continue to cause controversy, and here we add one more to the list.

If an atom, initially in an excited state, emits a photon and is later found in its ground state, when exactly did the transition take place? If the decay sets off a chain of events leading to the death of a cat6, how long ago did the cat die? This is another general problem in elementary quantum mechanics, and below we will address it, using the simplest model available. Here we take the view found, e.g., in7. For any observed sequence of events quantum mechanics provides a probability amplitude, essentially a matrix element of an unitary evolution operator between the states representing the observed conditions. Its absolute square yields the desired likelihood of seeing an outcome or outcomes. At the end of the experiment an observer has access to the atom’s condition, plus the record of the moment of decay, encoded into the clock’s (the cat’s) condition. Whether quantum mechanics can be expected to do more is, indeed, an open question beyond the scope of our paper.

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